I think that's something that has to be answered per individual artist, as opposed to a blanket statement.
For example, it's easier for me to separate Michael Jackson from Michael Jackson's music because his work largely was uninvolved the fukkery he may or may not have been involved in. Theoretically, someone could listen to a greatest hits collection from him, and have little to no reason to believe he might've been up to some wild shyt.
But for someone like Woody Allen, that's harder. One of his most revered movies is about him, as a 42 year old, engaging in a relationship with a 17 year old. That's fukking CRAZY considering the allegations against him, and that he found multiple ways to write/direct himself and others into May December style relationships and situations.